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Register a new userFree energy and entropy for finite temperature quantum field theory under the influence of periodic backgrounds
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Added by
Jose M Munoz-Castaneda
Publication date
2019
fields
Physics
and research's language is
English
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The basic thermodynamic quantities for a non-interacting scalar field in a periodic potential composed of either a one-dimensional chain of Dirac $delta$-$delta^prime$ functions or a specific potential with extended compact support are calculated. First, we consider the representation in terms of real frequencies (or one-particle energies). Then we turn the axis of frequency integration towards the imaginary axis by a finite angle, which allows for easy numerical evaluation, and finally turn completely to the imaginary frequencies and derive the corresponding Matsubara representation, which this way appears also for systems with band structure. In the limit case $T to 0$ we confirm earlier results on the vacuum energy. We calculate for the mentioned examples the free energy and the entropy and generalize earlier results on negative entropy.
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The thermodynamics of a scalar field with a quartic interaction is studied within the linear delta expansion (LDE) method. Using the imaginary-time formalism the free energy is evaluated up to second order in the LDE. The method generates nonperturbative results that are then used to obtain thermodynamic quantities like the pressure. The phase transition pattern of the model is fully studied, from the broken to the symmetry restored phase. The results are compared with those obtained with other nonperturbative methods and also with ordinary perturbation theory. The results coming from the two main optimization procedures used in conjunction with the LDE method, the Principle of Minimal Sensitivity (PMS) and the Fastest Apparent Convergence (FAC) are also compared with each other and studied in which cases they are applicable or not. The optimization procedures are applied directly to the free energy.
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